Decahelicene

or: introducing the sheep horn effect.

An experimental challenge: will this molecule racemize easily?

Helicenes are benzologues of phenanthrene.
With four or more rings (tetrahelicene, or [4] for short, pentahelicene [5],
etc.) the compounds exist in two helical, enantiomeric forms, with
C2 symmetry.
Racemization experiments, carried out in the seventies, gave surprising results
(see table). Not only
did racemization occur at lower temperatures than expected from hardware
models; the barriers even showed a tendency to level off for a higher number
of rings:

Racemization barriers (kcal/mol)

[4]

[5]

[6]

[7]

[8]

[9]

[10]

compounds

Experimental results

Grac

--

24.1

36.2

41.7

42.4

43.5

?

Hrac

--

22.9

35.0

40.5

41.0

41.7

?

Computational results

DFT-BLYP (ref. 2)

3.5

22.7

35.2

--

41.5

--

?

AM1 (ref. 1)

7.6

22.9

31.4

34.7

34.9

34.0

39.6?

(The structures in this table, and some other on this page, are linked
to .pdb files for local viewing.)

Very recently (more than twenty years after the measurements) three
groups,
remarkably close in space and time, but independently,
performed calculations on the
racemization process for the compounds [4] to [9], published in two papers:

The calculations confirmed that for [4] to [9] the racemization occurs
via a symmetric transition state (TS).
For [4] this TS is flat. In the larger compounds this is obviously not
possible and the TS adopts a kind of saddle shape, with Cs symmetry
(mirror plane).

This model explains why the energy barrier is not simply rising with an
increasing number of rings.
In the ground state, the helical forms with C2 symmetry,
the strain increases regularly with every
extra ring that is added.
In the Cs structures, this strain is more severe and
the barriers increase going from [4} to [7].
In the [7] TS however, the end rings are almost parallel to each other.
One or two extra rings added are hardly distorted and less extra strain
is introduced.
So one would expect the barrier to decrease rather than increase for a
higher number of rings, as is actually found in the calculations for
[8] and [9] (not in the experiment, however no error is given for these
measurements).

For [9], AM1 found next to this TS two more saddle points (mirror images
of eachother). These three saddle points were very close in energy, too
close to draw any conclusions on the exact nature of the 'true' transition
state. But it indicates that for the higher helicenes (>8) the transition state not
necessarily coincides with the symmetrical Cs structure.

What about the higher helicenes?

Decahelicene, to the best of my knowledge, has not been measured;
and it was not included in the calculations cited above.
On the one hand, the model presented here suggests that [10] could have a
barrier lower than that of nonahelicene.
On the other hand, larger values of n, the number of rings, introduce a new complication.
In the Cs structure, the end rings bend inside and approach the central part of
the molecule, as can be seen in the side view on the right.
It reminds me of the horns of certain types of sheep.

Calculations suggest that the Cs structure with the
mirror plane is relatively stable indeed,
even to such an extent that it becomes an intermediate, a local minimum,
33.7 kcal above the
helical ground state. A difference which is in between that of hexa- and
heptahelicene!
(Also calculated with AM1, which underestimates the experimental barrier.
Grimme (ref. 2) showed that DFT calculations are the most accurate for this
type of structures.)

This result implies that the actual transition state, the maximum in the
racemization path, is asymmetric.
The potential energy surface around the Cs structure appears to be
rather flat
with respect to the dihedral angles
defined along the inner rim of the helix.
On its way from Cs to helix the structure passes through a
conformation that resembles the [9]TS
(+ an extra benzene ring) and subsequently the [8]TS (+ a naphthalene unit
attached to one end, structure on the left).
Up to this point, the energy is still rising! Closer inspection reveals
that this is caused by the 'sheep horn' effect: the 'extra' naphthalene unit
is not flat anymore,
but forced outwards so as to avoid the central bridge. So while in the pure [8]TS the
energy falls when one end of the molecule rotates underneath the other end
on its way to the helix, in the [10}TS this is compensated for by the
strain in the other end of the molecule.

By approximation (what an AM1 calculation is anyway) the [10] transition state
(left) is some 5.9
kcal above the symmetric Cs structure (above, right), and the
calculated racemization barrier is
39.6 kcal/mol. This is much higher than calculated for [8] and [9].
Energy diagrams can be found on a separate page.

So, a question for the experimentalists, what is the 'real' value?
And, synthetic chemists, think of the nice
structures you can make if
you can trap the relatively stable intermediate and connect (photochemically?)
the two end rings,
lying side by side . . .
In the mean time we'll have to
continue our calculations using better, more laborious methods.

And, now we are at it, take dodecahelicene, or,
extrapolating even further, cut the coiled part of your telephone cord.....